The present invention relates to a registration technology between different images including the same subject.
As imaging apparatuses, there have heretofore been known, for example, a magnetic resonance apparatus (MR), a radiation tomography imaging apparatus (CT), an ultrasound apparatus, etc. These imaging apparatuses respectively have merits/demerits existing for every imaging modality and may be deficient in diagnosis accuracy only in an image by a specific imaging modality. Therefore, in recent years, attempts have frequently been made to improve diagnosis accuracy by performing a diagnosis using images based on a plurality of different imaging modalities.
In the diagnosis using the images by the different imaging modalities, image coordinate systems differ for every imaging modality. Therefore, a technology for correcting positional displacements due to the difference between these coordinate systems and variations/deformation of an organ, i.e., a technology for registration between images is important.
As a method of performing registration between a plurality of images different in imaging modality from each other, a method using mutual information is the most common (refer to, for example, IEEE Trans. on Med. Imaging, 16:187-198, 1997). This method is of an intensity based method based on the brightness value of an image in a broad sense. That is, it is a prerequisite that object images have to do with brightness values thereamong to perform registration using the mutual information.
In an ultrasound (US) image, however, an acoustic shadow occurs and hence a brightness value at the back of a high reflector is lowered more than the original value. The brightness value of each blood vessel also changes depending on the running direction of the blood vessel. Therefore, for example, in the registration between an MR image and a US image or the registration between a CT image and a US image, the situation in which brightness values have poor relevance often occurs. A feature based method other than the method based on the brightness values like the mutual information is suitable for such images.
As a typical example of the feature based method, there has been proposed a method using a normalized gradient field (NGF) (refer to, for example, Proceeding of SPIE Vol. 7261, 72610G-1, 2009). The normalized gradient field is that after primary partial differentiations (i.e., gradient vectors in respective directions x, y and z) have been calculated at coordinates on each image, the gradient vectors are normalized by their lengths (VectorNorm). That is, the normalized gradient field is a feature amount indicative of only the direction of gradient without depending on the magnitude of a pixel value or a brightness value and the magnitude of gradient. If the normalized gradient field in the same direction is generated at mutually corresponding positions in some two images, the positions of the two images can be assumed to be aligned. Thus, this method is capable of performing registering by optimizing the matching degree of the directions each indicated by the normalized gradient field.
The normalized gradient field n is mathematically described as follows:
                              n          ⁡                      (                          I              ,              p                        )                          :=                  {                                                                                                                ∇                                              I                        ⁡                                                  (                          p                          )                                                                                                                                                          ∇                                                  I                          ⁡                                                      (                            p                            )                                                                                                                                                      ,                                                                                                  if                    ⁢                                                                                  ⁢                                          ∇                                              I                        ⁡                                                  (                          p                          )                                                                                                      ≠                  0                                                                                                      0                  ,                                                            otherwise                                                                        Equation        ⁢                                  ⁢        1            
In the Equation 1, ΔI(p) indicates a gradient vector at a coordinate p of an image I. Further, ∥ΔI(p)∥ indicates the length (Norm) of the gradient vector. The coordinate p is composed of components of x, y and z.
As can be understood from the Equation 1, the normalized gradient field n itself is not capable of separating a gradient caused by a structure and a gradient caused by noise. Thus, in order to suppress the influence of the gradient caused by noise, the following method has been proposed in Proceeding of SPIE Vol. 7261, 72610G-1, 2009:
                                          n            ɛ                    ⁡                      (                          I              ,              p                        )                          :=                              ∇                          I              ⁡                              (                p                )                                                                                                      ∇                                  I                  ⁡                                      (                    p                    )                                                                                      ɛ                                              Equation        ⁢                                  ⁢        2                                                                                ∇                              I                ⁡                                  (                  p                  )                                                                          ɛ                :=                                                            ∇                                                      I                    ⁡                                          (                      p                      )                                                        T                                            ⁢                              ∇                                  I                  ⁡                                      (                    p                    )                                                                        +                          ɛ              2                                                          Equation        ⁢                                  ⁢        3                                ɛ        =                  η          ⁢                                                    ∫                Ω                            ⁢                                                [                                      ∇                                          I                      ⁡                                              (                        p                        )                                                                              ]                                ⁢                                                                  ⁢                                  ⅆ                  p                                                                                    ∫                Ω                            ⁢                                                          ⁢                              ⅆ                p                                                                        Equation        ⁢                                  ⁢        4            
where ε is a constant arbitrarily selected according to the amount of noise in an image. In the related art method, the noise term ε is set in accordance with the Equation 4, and the gradient vector is normalized in consideration of the noise term.
An evaluation function D taken to be a registration index is defined by the following equations (it may be defined by either one of them).D(T,R)=∫Ω<n(R,p),n(T,p)>2dp  Equation 5D(T,R)=∫Ω∥n(R,p)×n(T,p)∥2dp  Equation 6
In Equations 5 and 6, T and R respectively indicate two images targeted for registration. Equation 5 calculates an integrated value of the square of an inner product of two normalized gradient fields n(R,p) and n(T,p). Equation 6 calculates an integrated value of the square of an outer product of two normalized gradient fields n(R,p) and n(T,p).
In the image registration method using the above-mentioned normalized gradient fields, the vector caused by nose takes a small value on the normalized gradient field. Since, however, the evaluation functions take the integrated values of the inner products or the outer products at all coordinates as in Equations 5 and 6, it is not ignored how they will affect the evaluation functions if the absolute number thereof increases, even though they are individually small values. Therefore, the influence of gradient due to noise may not be eliminated sufficiently.
With the foregoing in view, there has been desired a registration method capable of more effectively suppressing the influence of gradient due to noise in registration between two images including the same subject.